Total 4-Choosability of Series-Parallel Graphs

It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours. Together with other known results, this shows that the List-Total-Colouring Conjecture, that ch (G) = (G) for every graph G, is true for all K4-minor-free graphs and, therefore, for all outerplanar graphs.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Douglas R. Woodall
• Keywords: Colours, COMBINATORICS 2006, K4-minor-free Graphs, Maximum Degree